"Erdős conjectured in 1975 that there do not exist three consecutive powerful integers." - Guy

See Guy for Erdős' conjecture and statement that this sequence is infinite. - Jud McCranie, Oct 13 2002

It is easy to see that this sequence is infinite: if n is in the sequence, so is 4*n*(n+1). - Franklin T. Adams-Watters, Sep 16 2009

The first of a run of three consecutive powerful numbers (conjectured to be empty) are just those in this sequence and A076445. - Charles R Greathouse IV, Nov 16 2012

Jaroslaw Wroblewski (see prime puzzles link) shows that there are infinitely many terms in this sequence such that neither a(n) nor a(n+1) is a square. - Charles R Greathouse IV, Nov 19 2012

Paul Erdős wrote of meeting Kurt Mahler: "I almost immediately posed him the following problem: ... are there infinitely many consecutive powerful numbers? Mahler immediately answered: Trivially, yes! x^2 - 8y^2 = 1 has infinitely many solutions. I was a bit crestfallen since I felt that I should have thought of this myself." - Jonathan Sondow, Feb 08 2015